Clinton has won three million more votes than her rival Bernie Sanders and is well ahead in the pledged delegate count.

Voters in six American states cast ballots on Tuesday in the final major primaries of the 2016 White House race, after media reported that Hillary Clinton secured enough delegates to win the Democratic nomination.

The results are expected to see Clinton declare victory as the first woman in history to secure the presidential nomination of a major US party, putting her on course for a showdown with New York billionaire Donald Trump, the presumptive Republican nominee, in November's election.

Her challenger Bernie Sanders has so far ignored media reports that she has clinched the magic number of delegates. The self-declared democratic socialist is chasing a win in the country's largest state California, and insisting the nominee will not be chosen until the party convention in July.

Voting was underway in six states - California, New Jersey, New Mexico, Montana, North Dakota and South Dakota. New Jersey and the Dakotas will be the first polls to close at 8:00pm Eastern time (0000 GMT Wednesday).

It remained unclear what effect the reports that Clinton had passed the milestone of 2,383 delegates Monday would have on those casting ballots.

Mired in scandal

"I'm a Bernie Sanders guy all the way," said 21-year-old student Saul Gomez, voting in Los Angeles. "Honestly he seems a lot more genuine to me," he said. "He's consistent, and I dig that."

Clinton - the 68-year-old former first lady, New York senator and for four years President Barack Obama's top diplomat - is scheduled to deliver a speech in Brooklyn late on Tuesday in perhaps the pinnacle of her political career to date.

It marks a dramatic resurgence for the woman often described as the most experienced US presidential candidate in generations, but who remains mired in scandal about her emails and perceptions of dishonesty - leaving her with unpopularity ratings surpassed only by the controversial Trump.

Her stiff campaigning style saw her lose to Obama in their 2008 nomination battle and has drawn stark contrast to the crowds of thousands of young people that 74-year-old Sanders has energised nationwide.

Clinton has refrained from getting too carried away by the US network tallies showing her capturing the nomination, urging her supporters to still come out and vote.

"We are on the brink of a historic, historic, unprecedented moment," she said in Long Beach, California. "But we still have work to do, don't we?"

On Tuesday, House Minority Leader Nancy Pelosi - who was the first woman speaker of the House of Representatives and is a California superdelegate this year - formally endorsed Clinton.

Tight Clinton-Sanders race

While polls predict a tight Clinton-Sanders race in California, a loss there would not prove fatal for her. Clinton has won three million more votes than Sanders and is well ahead in the pledged delegate count.

Her campaign manager said they would celebrate Tuesday night and then focus on unifying the party in a bid to defeat Trump.

"It will be time for the party to start to come together and make sure that we rally behind our nominee," Robby Mook told CNN.

"Senator Sanders and his campaign have achieved incredible things. They've brought so many people into the process... these people will be so important to winning the general election," Mook said.

Meanwhile Trump has come under hostile fire from fellow Republicans for making belligerent attacks on a judge presiding over a case against one of his business interests. Trump called him biased because he is of Mexican descent.

Republican House Speaker Paul Ryan on Tuesday called Trump's remarks "indefensible" and "the textbook definition of a racist comment," but still urged the party to unite for November.

"I think if we go into the fall as a divided party, we are doomed to lose," Ryan said.